This paper considers a multi-type fluid queue with priority service. The input fluid rates are modulated by a Markov chain, which is common for all fluid types. The service rate of the queue is constant. Various performance measures are derived, including the Laplace–Stieltjes transform and the moments of the stationary waiting time of the fluid drops and the queue length distributions. An Erlangization-based numerical method is also provided to approximate the waiting time and the queue length distributions up to arbitrary precision. All performance measures are formulated as reward accumulation problems during busy periods of simple Markovian fluid flow models, for which efficient matrix-analytic solutions are provided, enabling us to solve large models with several hundred states.

中文翻译：

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马尔可夫调制流体优先队列的等待时间和队列长度分析

本文考虑具有优先服务的多类型流体队列。输入流体速率由马尔可夫链调节，这对于所有流体类型都是通用的。队列的服务速率是恒定的。导出了各种性能度量，包括拉普拉斯-斯蒂尔捷斯变换和流体滴的平稳等待时间和队列长度分布的矩。还提供了一种基于 Erlangization 的数值方法来近似任意精度的等待时间和队列长度分布。在简单马尔可夫流体流动模型的繁忙时期，所有性能指标都被表述为奖励累积问题，为此提供了有效的矩阵分析解决方案，使我们能够解决具有数百个状态的大型模型。